이해가 안되요/이해하지 못헤요/이해하지 않아요 => 이해가 안돼요 / 이해하지 못해요 (이해하지 않아요 is a bad expression). * 이해가 안돼요 - "It doesn't make sense" - probably the most common expression. Note 되다 -> 되어요 -> 돼요. * 이해가 안 가요 - "It doesn't make sense; I can't make sense of it" - similar but more often used for technical things. * 이해(하지) 못해요 - "I can't/don't understand". But 이해 못하겠어요 sounds better. * 이해할 수(가) 없어요. - "I can't/don't understand". Similar to 이해 못하겠어요. * (BAD) 이해하지 않아요 - "I won't understand" - this doesn't make sense. It takes a deep knowledge of the language to understand all the different nuances of these expressions. For example, 돼요/안돼요 expresses how things naturally work more than one's intention, so 안돼요 is more natural than 안되겠어요. 가요 is similar. 못해요 on the other hand is often used as a phrase of a refusal even though it's original meaning is "can't". So 이해 못해요 sounds too strong and cold. 못하겠어요 expresses "I try but I can't understand it" much better. In 이해할 수 없어요, -ㄹ 수 없어요 is already close to 못하겠어요 in meaning, so we don't say -ㄹ 수 없겠어요. As you can see, Korean seems to have too many subtle and fine layers of meaning for this kind of simple statements. In the beginning, however, there's no need to worry too much about such subtleties.